# `di_pls` — Domain-Invariant PLS (di-PLS) _Group_: **Calibration transfer** · _Registry tolerance_: `1e-06` ## Description Domain-invariant PLS From the `pls4all.sklearn.DIPLSRegression` docstring: > Domain-invariant PLS (Nikzad-Langerodi 2018). > **Registry note** — Python `diPLSlib.models.DIPLS` (B-Analytics; Nikzad-Langerodi 2018 authors). pls4all `di_pls_fit` defaults to the diPLSlib algorithm (centered NIPALS, convex-relaxation penalty, target-mean rescale) — bit-for-bit parity with `DIPLS(centering=True, rescale='Target')`. Set `cfg.di_pls_legacy = 1` to fall back to the pre-0.97.4 SIMPLS direction projection. ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `n_components` | `int` | `2` | Number of latent components extracted (k). | | `di_lambda` | `float` | `1.0` | Domain-invariance penalty weight balancing covariance alignment vs response fit. | ## Explanations ### Bibliographic source Nikzad-Langerodi, R., Zellinger, W., Saminger-Platz, S. & Moser, B. A. (2018). *Domain-invariant partial-least-squares regression*. Analytical Chemistry 90(11), 6693–6701. ### Mathematical principle Calibration transfer methods reconcile spectra acquired on different instruments or under different environmental conditions. di-PLS does this by augmenting the PLS objective with a domain-discrepancy penalty: $\mathcal{L}(\mathbf{w}) = -\operatorname{Cov}(\mathbf{X}_s\mathbf{w}, \mathbf{y}_s)^2 + \lambda \,\mathrm{MMD}^2(\mathbf{X}_s\mathbf{w}, \mathbf{X}_t\mathbf{w})$, where $(\mathbf{X}_s, \mathbf{y}_s)$ is a labelled source domain, $\mathbf{X}_t$ is an unlabelled target domain and MMD is the maximum mean discrepancy. Minimising $\mathcal{L}$ produces latent directions $\mathbf{w}$ that simultaneously **predict $y$ in the source** and have **matched distributions across domains**. The model is therefore robust to drift between calibration and prediction sets without requiring labels on the target domain. Computational cost is dominated by the MMD term, which is $O((n_s + n_t)^2)$ in a naive implementation; pls4all uses a linear-kernel MMD which reduces this to $O((n_s + n_t) p)$. $\lambda$ controls the bias–transferability trade-off: $\lambda = 0$ recovers vanilla PLS on the source, large $\lambda$ shrinks toward a domain-aligned but potentially under-predictive model. ### Implementation `n4m_domain_adaptation_di_pls_fit` — requires `X_target` at fit time. Reference: Python `diPLSlib.models.DIPLS` (Nikzad-Langerodi authors). The pls4all variant matches diPLSlib's `rescale='Target'` source-centred default. R roxygen note (`sklearn_methods.R::di_pls`): > Domain-invariant PLS -- formula entry point. > @param X_target Numeric matrix for the target domain. > @param di_lambda Numeric DI-PLS penalty. > @inheritParams pls > @export MATLAB header (`bindings/matlab/+pls4all/DiPlsRegression.m`): ```text pls4all.DiPlsRegression Domain-Invariant PLS regression. ``` ### Usage Every pls4all binding tab dispatches into the same C kernel; the external libraries listed at the bottom of the page are the parity references registered in `benchmarks.parity_timing.registry`. Switch tabs to read the same fit in your language. The R package now ships drop-in-compatible facades for the CRAN `pls` package (`plsr`, `pcr`, `mvr`) and for the `mdatools::pls(x, y, ...)` matrix idiom — those tabs appear only on the methods that have a meaningful equivalence. **pls4all bindings** ::::{tab-set} :class: pls4all-bindings :::{tab-item} C ABI · libn4m :sync: c :class-label: lang-c ```c /* C ABI — libn4m */ n4m_context_t* ctx = n4m_context_create(); n4m_config_t* cfg = n4m_config_create(); n4m_method_result_t* res = NULL; n4m_domain_adaptation_di_pls_fit(ctx, cfg, &x_view, &y_view, /* hyperparams */, &res); /* … read coefficients / mask / scores via */ /* n4m_method_result_get_double_matrix / vector / scalar … */ n4m_method_result_destroy(res); n4m_config_destroy(cfg); n4m_context_destroy(ctx); ``` ::: :::{tab-item} Python · pls4all (raw) :sync: python-raw :class-label: lang-python ```python import pls4all from pls4all._methods import di_pls_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = di_pls_fit(ctx, cfg, X, y, n_components=4, X_target=X_target) # then: res.matrix("predictions"), res.matrix("coefficients"), # res.vector("mask"), res.scalar("intercept"), … ``` ::: :::{tab-item} Python · pls4all.sklearn :sync: python-sklearn :class-label: lang-python ```python from pls4all.sklearn import DIPLSRegression mdl = DIPLSRegression(n_components=2, di_lambda=1.0) mdl.fit(X, y, X_target=X_target) y_hat = mdl.predict(X_test) ``` ::: :::{tab-item} R · pls4all_method() :sync: r-dispatcher :class-label: lang-r ```r library(pls4all) # Unified low-level dispatcher (May 2026 R cleanup): res <- pls4all_method("di_pls", X, y, n_components = 4L, params = list(di_lambda = 1.0)) # res is a named list with MethodResult arrays/scalars. # selected_indices / top_k_intervals are 1-based. ``` ::: :::{tab-item} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- di_pls_fit(X_source, Y_source, n_components, X_target, di_lambda = 1.0) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} R · pls4all (formula+S3) :sync: r-formula :class-label: lang-r ```r library(pls4all) fit <- di_pls(y ~ ., data = train, ncomp = 4L) yhat <- predict(fit, newdata = test) summary(fit) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.di_pls(X, y, 4); % see header of bindings/matlab/+pls4all/di_pls.m for full % parameter surface: % res = di_pls(X_source, Y_source, n_components, X_target, di_lambda) yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab ```matlab mdl = pls4all.fit("di_pls", X, y, "NumComponents", 4); yhat = predict(mdl, Xtest); ``` ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.python_diplslib`** (python · python) — `diPLSlib` 2.5.0 · strict (rmse_rel ≤ 1e-06) — Python `diPLSlib.models.DIPLS` (B-Analytics; Nikzad-Langerodi 2018 authors). Same di-PLS penalty applied during deflation; centering / target rescaling differ slightly, so tolerance is widened. ::: ### Benchmarks Adaptive wall-clock per cell measured against [`full_matrix.csv`](../benchmarks/overview.md). Only backends that implement this method are listed; libraries without the method are omitted. **Verdict**  ·  ✓ ref / ≈ ref / ~ shape mark a reference-gate pass at strict / relaxed / qualitative tolerance  ·  ✓ bind = pls4all binding agrees with the C++ baseline  ·  ⇄ cross-check = documented by-design selector/RNG/model, noncanonical API/facade convention, or secondary oracle  ·  ✗ divergent  ·  ⚠ error  ·  — not run. The fastest backend per column is marked 🏆. **Reference gate**: strict — numeric equivalence (`rmse_rel_tol ≤ 1e-06`). Rows tagged with **📐** are the canonical parity references for this method (declared in [`parity_timing.registry`](../benchmarks/methodology.md)). C++ and external rows show reference parity; pls4all language bindings show binding parity against the C++ backend. Hover the icon for role and tolerance band. ::::{tab-set} :class: parity-tabs :::{tab-item} 1 thread :sync: threads-1
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 8e-152.58 ms🏆
Python · pls4all
pls4all.python✓ bind2.74 ms
pls4all.sklearn✓ 4e-152.82 ms
R · pls4all
pls4all.R✓ 6e-159.69 ms
pls4all.R.formula✓ 6e-1512.4 ms
pls4all.R.mdatools✓ 6e-1512.8 ms
pls4all.R.pls✓ 6e-1512.4 ms
Python · external
📐ref.python_diplslibsource3.78 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 8e-152.80 ms
Python · pls4all
pls4all.python✓ bind2.70 ms🏆
pls4all.sklearn✓ 4e-152.98 ms
R · pls4all
pls4all.R✓ 6e-159.91 ms
pls4all.R.formula✓ 6e-1512.2 ms
pls4all.R.mdatools✓ 6e-1512.9 ms
pls4all.R.pls✓ 6e-1511.2 ms
Python · external
📐ref.python_diplslibsource3.79 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 8e-152.74 ms🏆
Python · pls4all
pls4all.python✓ bind2.82 ms
pls4all.sklearn✓ 4e-152.95 ms
R · pls4all
pls4all.R✓ 6e-1511.1 ms
pls4all.R.formula✓ 6e-1514.0 ms
pls4all.R.mdatools✓ 6e-1513.0 ms
pls4all.R.pls✓ 6e-1512.4 ms
Python · external
📐ref.python_diplslibsource3.92 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)